Ur question is ambiguous and I do not know what u exactly mean, but I give some general comment.

Assume that interpolation to node P is desired and we have other N points in its neighborhood of this point, interpolation has the following form:

U(P) = Sigma_{over_support_set} w_i U_i

U(P) is desired value, U_i is value of each neighbor. Sometimes contribution of node P is also included (e.g. iterative procedures or transient analysis), this may leads to implicit system or explicit system (simple interpolator)

This formula is simplified (algebraic) form of any numerical method (FEM, FVM, meshless, &hellip. The distinction between various methods is related to method of determination of w_i and selection of support set.

For example in FEM w_i is computed by element-wise integration and addition of contribution of each element to node P (element that make a patch around P), then integration is converted to algebraic summation (computation of w_i) by (usually) application Gaussian quadrature method. In FDM, w_i terms are computed with the aide of Taylor expantion around node P (one dimensional, split method, or multi-dimensional un-split method). In meshless methods w_i is usually computed by using appropriate integration kernel. In these method number of support nodded could be arbitrary and explicit topology is ot required. And topology of support set could be varied within simulation.

In your problem: if topology of support set is fixed, you could construct the mentioned computational stencil by generalized FDM or formal FEM method (connection point of multi-block could be considered as a FEM node). If you look for a general method you could use meshless method which include variety of methods (these methods are interesting when topology of support set is varied and number of contributing points is changed).

Is your code cell-centered or node-centered? In cell-centered FVM, the value at this node should have contributions from four cells. In each block, you get the stencil and the variables at the three cells from the other three blocks, you are done. If it is done correctly, the node's value should be the same in all four blocks.